© 2018

The Kurzweil-Henstock Integral for Undergraduates

A Promenade Along the Marvelous Theory of Integration


Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alessandro Fonda
    Pages 1-59
  3. Alessandro Fonda
    Pages 61-123
  4. Alessandro Fonda
    Pages 125-173
  5. Back Matter
    Pages 175-222

About this book


This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.


integration kurzweil–henstock integral riemann sums fundamental theorem of calculus lebesgue integral differential forms gauss formula stokes–cartan formula banach–tarski paradox

Authors and affiliations

  1. 1.Dipartimento di Matematica e GeoscienzeUniversità degli Studi di TriesteTriesteItaly

About the authors

Alessandro Fonda, Università degli Studi di Trieste, Italy.

Bibliographic information

  • Book Title The Kurzweil-Henstock Integral for Undergraduates
  • Book Subtitle A Promenade Along the Marvelous Theory of Integration
  • Authors Alessandro Fonda
  • Series Title Compact Textbooks in Mathematics
  • Series Abbreviated Title Compact Textbooks in Mathematics
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-95320-5
  • eBook ISBN 978-3-319-95321-2
  • Series ISSN 2296-4568
  • Series E-ISSN 2296-455X
  • Edition Number 1
  • Number of Pages X, 216
  • Number of Illustrations 19 b/w illustrations, 5 illustrations in colour
  • Topics Real Functions
    Measure and Integration
  • Buy this book on publisher's site


“The author maintains here the exposition at a very didactic level, trying to avoid as much as possible unnecessary technicalities, which is a big advantage of this book. … In my point of view, the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMath 1410.26007, 2019)